Without a ground invasion and occupation force, and without removing the fanatical military leaders of Japan, the war would have continued in whatever way Japan could (and still would) produce men and materiél to fight. (Japan had no naval ships at the time of its surrender, so that was not an option, but they were still producing and flying kamikaze aircraft.)
The point is that the Japanese leadership absolutely had to be replaced. The “conventional aerial attacks” that @Qingu mentions (which were every bit as deadly as he says) did not have a significantly adverse effect upon the leadership. They knew that the American air war was very costly in terms of logistics alone – the number of planes and crews, the fuel required for the raids and the staging on western Pacific islands, and supply lines needed to keep all of that in place was very expensive.
At that point in history no “air war” had ever won a war. (In fact, after the war, investigators on the ground in Germany and Japan were astonished to find how ineffective low-level daylight bombing was at stopping war production, even when strictly military targets were chosen. Even the stunning show of air superiority mounted by the Allies in the Persian Gulf War and the “shock and awe” campaign of 2003 failed to kill the Iraqi military machine.) Even to this point in history, “air wars” do not “win” wars. Ground troops are still required.
The Japanese military leaders were confident that a ground invasion would absolutely be required. With their total propaganda campaign, they had a broad base of citizen support. Soldiers were not allowed to surrender, even those who had an inclination to do so. It was only when the Americans demonstrated clearly what could be done with single airplanes dropping single weapons – twice – that it was made perfectly clear to the leadership, and finally to the Emperor himself, that the war could not continue without even worse asymmetric Japanese casualties. The ratios had gone from “hundreds of American dead to each Japanese” (in the kamikaze attacks), to “tens of thousands of Japanese killed – to not a single American flyer”, and at “sustainable cost” to the Americans.
Anyone could do that math.
The Russians were not a factor until the Japanese capitulation was all but signed off.